URAL 2003. Simple Magic(数学啊 )

题目链接：http://acm.timus.ru/problem.aspx?space=1&num=2003

2003. Simple Magic

Time limit: 1.0 second

Memory limit: 64 MB

Do you think that magic is simple? That some hand-waving and muttering incomprehensible blubber is enough to conjure wonderful gardens or a fireball to burn your enemies to ashes?

The reality is a little more complicated than that. To master skills, young wizards spend years studying such subjects as magical analysis and demonology practice.

In fact, Oleg, a student of the Institute of Magic and Common Sorcery (IMCS) is preparing for an exam. And there’s no way he can calculate the Dumbledore determinant. As you might have guessed, he asked
you to help him.

Let us remind you the basic definitions just in case you haven’t been visiting lectures on the theory of nonlinear spells. The Gandalf theorem states that any part of subspace can be represented as
a vector of magic potentials that is an array of n positive integers. A Dumbledore determinant of this array equals the minimum number of elementary magical transformations required to turn the original array into the array where all elements are
equal to one. One elementary magical transformation turns the original array of length k into a new array of length k · (k ? 1) / 2. The elements of the new array are greatest common divisors of each pair of elements of the original
array. For example, the elementary magical transformation of array {2, 3, 3, 6} turns it into array {gcd(2, 3), gcd(2, 3), gcd(2, 6), gcd(3, 3), gcd(3, 6), gcd(3, 6)}, that is {1, 1, 2, 3, 3, 3}.

Input

The first line contains number n that is the length of the original array (3 ≤ n ≤ 10 000). Next nlines contain the elements of array that are positive integers not exceeding
107.

Output

Output Dumbledore determinant for the array given in the input. If Dumbledore determinant is not defined or it exceeds 1018,
output “infinity”.

Samples

3
1
2
3

1

4
2
2
2
2

infinity

Problem Author: Kirill Borozdin

Problem Source: Ural Regional School Programming Contest 2013

题意:

问是否能按照类似：array {2, 3, 3, 6} turns it into array {gcd(2, 3), gcd(2, 3), gcd(2, 6), gcd(3, 3), gcd(3, 6), gcd(3, 6)}, 的方式，求所给数组！

代码如下：

#include <cstdio>
#include <cmath>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
#define INF 0x3f3f3f3f
int a[10000047];
int main()
{
    int n;
    int num;
    while(~scanf("%d",&n))
    {
        memset(a, 0,sizeof(a));
        int ans = -INF;
        for(int i = 0; i < n; i++)
        {
            scanf("%d",&num);
            int k = sqrt(num*1.0);
            for(int i = 2; i <= k; i++)//质因子
            {
                if(num%i == 0)
                {
                    a[i]++;
                    ans = max(ans,a[i]);
                    while(1)
                    {
                        if(num%i == 0)
                        {
                            num/=i;
                        }
                        else
                        {
                            break;
                        }
                    }
                }
            }
            if(num != 1)
            {
                a[num]++;
            }
            ans = max(ans,a[num]);
        }
        if(ans == 1)
        {
            printf("1\n");
        }
        else if(ans == 2)
        {
            printf("2\n");
        }
        else if(ans == 0)
        {
            printf("0\n");
        }
        else
        {
            printf("infinity\n");
        }
    }
    return 0;
}